Hunter's theorem ensures that the complete homogeneous symmetric (CHS) polynomials of even degree are positive definite functions. We provide new proofs of Hunter's theorem, applications to operator theory, and a […]
Virtual links can be represented as equivalence classes of Gauss diagrams under Reidemeister moves. The Forbidden Moves are moves which look plausible but change the virtual isotopy class of the […]
We will examine the multiplicative structure of two skein algebras--- the usual Kauffman bracket skein algebra of a surface (generated by loops) and a generalization of it due to Roger-Yang […]
This is a talk in two parts covering two projects that the speaker mentored over the summer of 2025. The first project deals with the study of polytopes that arise […]
The classical Siegel's lemma (1929) asserts the existence of a nontrivial integer solution to an underdetermined integer homogeneous linear system, whose "size" is small as compared to the size of […]
Hecke algebras play a central role in both number theory and representation theory. While some Hecke algebras have explicit descriptions in terms of generators and relations, others are understood through […]
A key problem in computer proofs based on solutions from copositive optimization, is checking whether or not a given quadratic form is completely positive or not. In this talk we describe […]
A low autocorrelation binary sequence of length $\ell$ is an $\ell$-tuple of $+1$s and $-1$s that does not strongly resemble any translate of itself. Such sequences are used in communications and remote sensing for synchronization and ranging, where translation represents time delay. A single number that indicates how good a sequence is for such purposes, […]
In this talk, I'll attempt to give a friendly introduction to tropical linear series and explore their relationship to matroid theory. Along the way, we'll stop to admire the beautiful view […]
Inspired by the categorification program for a numerical invariant of three-manifolds, series invariants for closed manifolds and for knot complements were introduced. This in turn motivated an extension of the […]
Diophantine avoidance has been studied by several authors in recent years. This refers to effective results on existence of points of bounded size in a given algebraic set avoiding some […]
One of the key objects used in Ngo's proof of the fundamental lemma is the group scheme of universal centralizers associated to a split reductive group G. In this talk, we'll discuss forthcoming work, […]
